A quadrilateral has two diagonals that intersect at point O. Answer the following questions about this situation.
(i) State the converse of the property that "the diagonals of a parallelogram bisect each other".
(ii) Explain, with logical reasoning, how the fact that AO=OC and BO=OD (where A,B,C,D are the vertices taken in order) ensures that opposite sides of the quadrilateral are both equal and parallel. Hence give the special name that must be assigned to the quadrilateral.